>Is there an issue with me changing location to where I want to work and explaining to recruiters that I'm not currently living there but will be?

That will depend on each recruiter and if they decide they like that or not. A recruiter may think you actually live some place and go through interviews, etc., only to find out that you *don't* actually live there. This may be disappointing for some recruiters that did not wanted that to happen, and could be a waste of their times.

Personally I would not do so, as it may be a bit deceiving for my taste, specially if you put a place that you actually are not thinking on living, just with the hopes to get a work there and *then* be relocated.

However, I see no problem doing what you say *if* you actually are going to or had lived there recently.